A Method For Extracting cos\alpha

TL;DR

This paper proposes a novel method to extract the weak mixing angle alpha by analyzing B meson decay rates, utilizing interference effects and advanced theoretical calculations to improve precision in determining cos(alpha).

Contribution

It introduces a new approach combining Ward identities and operator product expansion to compute long-distance contributions without light cone wave functions for high q^2 values.

Findings

Branching fraction estimated at ~10^{-8} for q^2 > 2 GeV^2.

Differential decay rate highly sensitive to cos(alpha) at small q^2.

Method reduces reliance on light cone wave functions for theoretical calculations.

Abstract

We show that it is possible to extract the weak mixing angle alpha via a measurement of the rate for B^+(-) -> \pi^+(-) e^+e^-. The sensitivity to cos(alpha) results from the interference between the long and short distance contributions. The short distance contribution can be computed, using heavy quark symmetry, in terms of semi-leptonic form factors. More importantly, we show that, using Ward identities and a short distance operator product expansion, the long distance contribution can be calculated without recourse to light cone wave functions when the invariant mass of the lepton pair, q^2, is much larger than LQCDs. We find that for q^2 > 2 GeV^2 the branching fraction is approximately 1 * 10^{-8}|V_{td}/0.008|^2. The shape of the differential rate is very sensitive to the value of cos(alpha) at small values of q^2 with dGamma /dq^2 varying up to 50% in the interval -1< cos(alpha)< 1 at q^2= 2 GeV^2. The size of the variation depends upon the ratio V_{ub}/V_{td}.